Abstract-Small ultra high frequency (UHF) radio frequency identification (RFID) tags of fragmenttype structure can be designed for broadband operation and for versatile impedance matching to different chips. The fragment-type tag structure can be optimized by using genetic algorithm. In our design, multi-objective evolutionary algorithm based on decomposition combined with enhanced genetic operators (MOEA/D-GO) is used for optimization searching. The multiple objectives are defined in terms of power transmission coefficients for operation in multiple RFID bands and for impedance matching to several prevailing RFID chips. For demonstration, a fragmented tiny square UHF tag of dimensions of 5.5 mm * 5.5 mm is designed for multi-band operation over the 433 MHz, 869 MHz and 915 MHz RFID bands, and a fragmented round tiny RFID tag of radius of 4.5 mm is also designed for versatile connection to five prevailing RFID chips at 915 MHz. The tiny round versatile tag is tested by connecting two chips, the IMPIMJ Monza-4 chip (11 − 143j) and ALIEN Higgs-3 chip (27 − 195j), respectively. Effects of input impedance and adjunct fragments on versatility of the design are further discussed.